Answered: Part b and c of the question: Part b:…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 6E

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Question

Part b and c of the question:

Part b: Find the mean number of hurricanes.

(Type an integer or decimal rounded to three decimal places as needed)

Part c: Assuming the Poisson distribution and using the mean number of hurricanes per season from part b, compute the probabilities of experiencing 0-12 hurricanes in a season. Compare these to your answer to part a. How accurately does a Poisson distribution model this phenomenon? Construct a chart to visualize these results.

Start by computing the probablities assuming a Poisson distribution.

(Type an integer or decimal rounded to three decimal places as needed)

The number and frequency of a certain ocean's hurricanes annually from 1930 through 2005 is shown below. This means, for instance, that no hurricanes occurred
during 5 of these years, only one hurricane occurred in 16 of these years, and so on. Complete parts a through c below.
Number
1
4
7
8
9.
12 D
Frequency
16 20 10
4
1
1
...
a. Find the probabilities of 0–12 hurricanes each season using these data.
Number
1
2
4
6.
7
9.
12
Frequency
16
20
10
4
1
1
Probability
(Type integers or decimals rounded to three decimal places as needed.)
LO
O 5

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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